The alchemy of terminology, symbols, and signs ...

Or, 'What is a nurse doing … in a chemistry class?' [Ack. See Estrada]

In reading, I was reminded that chemistry adopted mathematical symbols for its own use. Not only that, but as a core science (with physics and biology, emerging from natural philosophy) there is a historical development from the time of alchemy:

Please see (with a graphical abstract):

C.Wentrup, The Transition from Alchemical to Modern Chemical Symbolism: from Bergman and Guiton de Morveau to Hassenfratz and Adet, Higgins, Richter, Dalton, and Berzelius. ChemPlusChem. 2024, 89, e202400033. https://doi.org/10.1002/cplu.202400033

This journey matters today as the use of symbols, in mathematics or other fields can be a barrier to learning and hence personal and disciplinary progress:

Ollie Hunter. Lost in translation: Demystify scientific symbolic language to help your chemistry students overcome any potential learning barriers. Royal Society of Chemistry, 23 May 2022.

As acknowledged many times, it is easy to take a word, or concept from one discipline and 'fit' it to - or in another. Or is it? Estrada concludes:

“The complexities of modern science and modern society have created a need for scientific generalists, for men trained in many fields of science.” This is a paradigm of science in the XXI century, where the advent of such fields like the study of complex systems requires multidisciplinary approaches. But the previous phrase was not written in the XXI century. It is the starting sentence in The education of a scientific generalist” published in Science in 1949 (Bode et al. 1949).' p.161. 

'Mathematics has been defined as the science of patterns. Thus, mathematicians search for “numerical patterns, patterns of shape, patterns of motion, patterns of behavior, voting patterns in a population, patterns of repeating chance events, and so on” (Byers 2010). Once a pattern is identified either in chemistry or in mathematics, the researcher can proceed to the clarification of the systematic rule which is behind that pattern. This is evident in the analogy used here between code-breaking and structure elucidation. This attachment to patterns makes both chemists and mathematicians very prone to the use of pictures. An organic chemist hardly can say anything about the chemical reactivity (or any physical or chemical property) of a molecule from its exact quantum-mechanical Hamiltonian. However, she will construct a complete narrative about the physical and chemical properties of a molecular structure drawn in a piece of paper, even if such a molecule is completely imagined. The power of pictures in mathematics is discussed in the book Mathematics and the Unexpected by Ivar Ekeland (1990) where its value is recognized as fundamental in the early stages of the development of mathematical ideas. This also introduces a very important analogy among chemists and mathematicians. Namely, that they use a proper language in their respective fields. While physicists use the mathematical language in their investigations, chemists use the sophisticated language of chemical formulas and specific symbols to represent charges, rearrangements, partial equilibria, etc. These “invented” languages mainly appear only in Chemistry and in Mathematics, making them unique intellectual activities.' p.162.

With thanks to the author, Ernesto Estrada IFISC for additional thoughts and insights:

Estrada, E. What is a mathematician doing…in a chemistry class?. Found Chem 26, 141–166 (2024). https://doi.org/10.1007/s10698-023-09497-4